Power supply for a pulsed load

ABSTRACT

A power supply ( 1 ) for a pulsed load ( 2 ) includes a first energy storage device in the form of a battery ( 3 ) which is in parallel with a second energy storage device in the form of a supercapacitor ( 4 ). Battery ( 3 ) and supercapacitor ( 4 ) are respectively modelled as: 
     an ideal battery ( 7 ) in series with an internal resistance ( 8 ); and 
     an ideal capacitor ( 9 ) in series with an equivalent series resistance (ESR) ( 10 ). 
     Through use of a supercapacitor ( 4 ) having a low ESR with respect to the resistance ( 8 ), the power supply ( 1 ) facilitates continuity of supply to load ( 2 ). That is, during peak demand more of the load current will be supplied by supercapacitor ( 4 ) due to the lower ESR. Moreover, during times of lower load current demands the battery recharges the supercapacitor. This reduces the peak current needed to be provided by the battery and thereby improves battery longevity.

FIELD OF THE INVENTION

The present invention relates to a power supply.

The invention has been developed primarily for use with mobiletelephones and will be described hereinafter with reference to thatapplication. It will be appreciated, however, that the invention is notlimited to that particular field of use and is also suitable for otherelectronic devices, particularly portable devices such as Notebookcomputers, palmtop computers, electronic organisers, two-way pagers,remotely powered electronic device and the like.

BACKGROUND OF THE INVENTION

Pulsed loads occur in many battery-powered portable devices and the peakcurrent may be many times the resting current. When the battery isnearly flat or is old, its' effective internal resistance tends toincrease, and it is less able to supply peak current demand without thedevice cutting out. Heavy load pulses generally also cause a largevoltage drop when they occur, and this may be detrimental to thebattery. Lithium-ion batteries are particularly susceptible to damage inthis way.

As a result, pulse loads invariably reduce battery run-time as the loadwill have a minimum threshold supply voltage required at all times. Whenthe load pulses and that voltage drop below the minimum threshold, theelectronic device must shut down as the voltage regulating circuitry isno longer able to supply the necessary voltage to run key circuits.However, at this time there may be useful energy remaining in thebattery.

Moreover, some portable devices include protection circuitry that shutsthe device down if the current drawn from the battery exceeds apredetermined threshold. While this circuitry is designed to protect thebattery, it also results in shut down of the device when the peakcurrent, although being over the threshold, was so for only a shortperiod. This then requires the device to be restarted and, in some,cases, reconfigured. For mobile telephone and personal computingapplications this is a source of frustration to users.

Any discussion of the prior art throughout the specification should inno way be considered as an admission that such prior art is widely knownor forms part of common general knowledge in the field.

DISCLOSURE OF THE INVENTION

It is an object of the invention, at least in the preferred embodiment,to overcome or substantially ameliorate at least one of thedisadvantages of the prior art, or at least to provide a usefulalternative.

According to a first aspect of the invention there is provided an energystorage device including:

a battery having a predetermined internal resistance R and two terminalsfor allowing electrical connection to the battery, and

a supercapacitor connected in parallel with the terminals and having apredetermined equivalent series resistance ESR, where ESR<0.25.R.

Preferably, the ESR<0.1.R.

Preferably also, the device supplies a load with a pulsed load profile,wherein the capacitance provided by the supercapacitor is sufficient tolimit the battery current to a predetermined maximum. More preferably,the supercapacitor provides a substantially constant current as theenergy storage device discharges.

In a preferred form, the device includes a housing for containing boththe battery and the supercapacitor, the terminals being accessible fromoutside the housing for connecting to a load.

According to a second aspect of the invention there is provided a powersupply for a portable electronic device, the power supply including anenergy storage device according to the first aspect and supply rails forengaging the terminals of the energy storage device.

Preferably, the supply rails selectively engage the terminals. Morepreferably, the terminals are moved out of engagement with the supplyrails to allow the like terminals of a like energy storage device to bemoved into engagement with the supply rails.

According to a third aspect of the invention there is provided an energystorage device including:

a battery for providing a battery current and having two terminals forelectrically connecting with a load; and

a supercapacitor connected in parallel with the terminals and having apredetermined capacitance that, in use, limits the battery current to apredetermined threshold.

Preferably, the load draws a pulsed current from the energy storagedevice

According to a fourth aspect of the invention there is provided a powersupply including:

a battery for providing a battery current and having two terminals forelectrically connecting with a load that demands a pulsed current; and

a supercapacitor connected in parallel with the terminals formaintaining the ratio of the RMS value of the battery current and theaverage value of the battery current at less than about 1.5.

Preferably, the supercapacitor maintains the ratio of the RMS value ofthe battery current and the average value of the battery current at lessthan about 1.3. More preferably, the supercapacitor maintains the ratioof the RMS value of the battery current and the average value of thebattery current at less than 1.1.

According to a fifth aspect of the invention there is provided an energystorage device including:

a battery for providing a battery current and having two terminals forelectrically connecting with a load that demands a pulsed current; and

a supercapacitor connected in parallel with the terminals formaintaining the ratio of the RMS value of the battery current and theaverage value of the battery current at less than about 1.5.

Preferably, the supercapacitor maintains the ratio of the RMS value ofthe battery current and the average value of the battery current at lessthan about 1.3. More preferably, the supercapacitor maintains the ratioof the RMS value of the battery current and the average value of thebattery current at less than 1.1

According to a sixth aspect of the invention there is provided a powersupply including:

a battery having two terminals for electrically connecting with a loadthat demands a pulsed current; and

a supercapacitor connected in parallel with the terminals formaintaining the ratio of the range of instantaneous power provided bythe battery and the average value of the power provided by the batteryat less than a predetermined threshold.

Preferably, the the predetermined threshold is one of the following:1.5; 1; and 0.3.

According to a seventh aspect of the invention there is provided anenergy storage device including:

a battery having two terminals for electrically connecting with a loadthat demands a pulsed current; and

a supercapacitor connected in parallel with the terminals formaintaining the ratio of the range of instantaneous power provided bythe battery and the average value of the power provided by the batteryat less than a predetermined threshold.

Preferably, the predetermined threshold is one of: 1.5; 1; and 0.3.

According to an eighth aspect of the invention there is provided anenergy storage device including:

a battery having a predetermined internal resistance R and two terminalsfor allowing electrical connection to the battery, and

a supercapacitor connected in parallel with the terminals and having apredetermined equivalent series resistance ESR and a capacitance C,where ESR<0.5.R and C is less than 1 Farad.

According to a ninth aspect of the invention there is provided an energystorage device including:

a battery having a predetermined internal resistance R and two terminalsfor allowing electrical connection to the battery; and

a supercapacitor connected in parallel with the terminals and having apredetermined equivalent series resistance ESR, where ESR<110 mOhms<R.

Preferably, the ESR is less than about 50 mOhms. More preferably, theESR is less than about 30 mOhms.

According to a tenth aspect of the invention there is provided an energystorage device including:

a battery having a predetermined internal resistance R and two terminalsfor allowing electrical connection to the battery; and

a supercapacitor connected in parallel with the terminals and having apredetermined equivalent series resistance ESR, a predetermined volume Vand a predetermined capacitance C, where ESR<0.5.R, V<14 cm³ and C>1Farad.

According to an eleventh aspect of the invention there is provided anenergy storage device including:

a battery having two terminals for allowing electrical connection to thebattery; and

a supercapacitor having a plurality of serial connected supercapacitorcells for connecting in parallel with the terminals, wherein thesupercapacitor cells have an operating voltage of at least 2.3 Volts andthe supercapacitor has a predetermined equivalent series resistance ESRof less than about 20 mOhms.

Preferably, the ESR is less than about 15 mOhms.

According to a twelfth aspect of the invention there is provided anenergy storage device including:

a battery having two terminals for allowing electrical connection to thebattery; and

a supercapacitor having a plurality of serial connected supercapacitorcells for connecting in parallel with the terminals, wherein thesupercapacitor cells have an operating voltage of at least 2.3 Volts andthe supercapacitor has a predetermined capacitance of greater than about1.9 Farads.

BRIEF DESCRIPTION OF THE DRAWINGS

Preferred embodiments of the invention will now be described, by way ofexample only, with reference to the accompanying drawing in which:

FIG. 1 is a schematic view of a power supply according to the invention;

FIG. 2 is a schematic view of the power supply of FIG. 1 illustratingthe internal resistance of the battery and the equivalent seriesresistance of the supercapacitor;

FIG. 3 is a chart demonstrating the discharge of a battery “with” andwithout a supercapacitor in parallel;

FIG. 4 is a sample of one of the discharge cycles of FIG. 3;

FIG. 5 is a schematic illustration of the transients that are generatedin the power supply of a typical notebook computer;

FIG. 6 is a sample of the voltage and current waveforms in a powersystem of the Intel® Whidbey Notebook Platform without a supercapacitor;

FIG. 7 is a sample of the voltage and current waveforms in a powersystem of the Intel® Whidbey Notebook Platform with a supercapacitor inparallel with the battery;

FIG. 8 is a graph of the instantaneous power drawn from a battery for anotebook computer with and without a parallel supercapacitor;

FIG. 9 is a table that provides two additional examples ofsupercapacitors that are applicable for use in a power supply accordingto the invention;

FIG. 10 is a graph of the modelled performance of a power supplyaccording to the invention for use with a GSM mobile telephone load anda 50 second call cycle;

FIG. 11 is a graph of the modelled performance of a power supplyaccording to the invention for use with a GSM mobile telephone load anda 5 second on-time;

FIG. 12 is a graph of the modelled performance of a power supplyaccording to the invention for use with a GSM mobile telephone load anda 10 second on-time;

FIG. 13 is a graph of the modelled performance of a power supplyaccording to the invention for use with a GSM mobile telephone load anda 20 second on-time;

FIG. 14 is a graph of the modelled performance of a power supplyaccording to the invention for use with a GSM mobile telephone load anda 50 second on-time;

FIG. 15 is a table illustrating the use of the invention;

FIG. 16 is a drawing that is referred to in Annexure 1 as “FIG. 1”;

FIG. 17 is a drawing that is referred to in Annexure 1 as “FIG. 2”;

FIG. 18 is a drawing that is referred to in Annexure 1 as “FIG. 3”;

FIG. 19 is a drawing that is referred to in Annexure 1 as “FIG. 4”;

FIG. 20 is a drawing that is referred to in Annexure 1 as “FIG. 5”;

FIG. 21 is a drawing that is referred to in Annexure 1 as “FIG. 6”;

FIG. 22 is a drawing that is referred to in Annexure 1 as “FIG. 7”; and

FIG. 23 is a drawing that is referred to in Annexure 1 as “FIG. 8”.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The following terms are used in the specification in the followingmanner:

1. “laptop computer” and “notebook computer” are used interchangeablyand are intended to include portable computing devices, particularlythose having on board rechargeable energy storage devices;

2. “supercapacitor” is used to designate an energy storage device thatstores energy in the electric fields established at the interfacebetween an electrolyte and a plurality of electrodes; and

3. “battery” is used to designate an energy storage device that storesenergy electrochemically.

Referring to FIG. 1, a power supply 1 for a pulsed load 2 includes afirst energy storage device in the form of a battery 3 which is inparallel with a second energy storage device in the form of asupercapacitor 4. As best shown in FIG. 2, battery 3 and supercapacitor4 are respectively modelled as:

an ideal battery 7 in series with an internal resistance 8; and

an ideal capacitor 9 in series with an equivalent series resistance(ESR) 10.

Through use of a supercapacitor 4 having a low ESR with respect to theresistance 8, the power supply 1 facilitates continuity of supply toload 2. That is, during peak demand more of the load current will besupplied by supercapacitor 4 due to the lower ESR. Moreover, duringtimes of lower load current demands the battery recharges thesupercapacitor. This reduces the peak current needed to be provided bythe battery and thereby improves battery longevity.

That is, this parallel hybrid combination of a supercapacitor and abattery allows a reduction in the voltage excursions under load,permitting the load to operate reliably until most of the battery'senergy has been used. This helps to protect the battery from potentiallydamaging voltage drops, of particular benefit to Lithium-ion batteries.

Conventional capacitors usually cannot support such loads for more thana few milliseconds. The supercapacitors used in the present embodiments,however, have high capacitances so that, for a given load current, thepeak current drawn from the battery will be limited.

Use of a hybrid battery-supercapacitor power supply, as envisaged by theinvention, allows significantly better performance than can be achievedthrough use of a battery alone. Partly this is due to the much lowereffective internal resistance that is offered by the supercapacitor, butalso due to the large capacitances that are provided.

The characteristics of the supercapacitor will, in part, be driven bythe battery and the load characteristics. However, it is preferred thatuse is made of carbon double layer supercapacitors with offer very highcapacitance—from a few mF to hundreds of Farads—low Equivalent SeriesResistance (ESR)—1 mΩ and up—and low leakage currents—just a few μA.Such supercapacitors allow the design and implementation of improvedpower supplies for portable devices that rely upon batteries as aprimary source of energy storage.

The supercapacitors used in the preferred embodiments come in a varietyof shapes, sizes and packaging to fit the space available. Oneparticularly preferred form is a thin prismatic form. Examples of suchsupercapacitors are provided in PCT patent application noPCT/AU99/01081, the disclosure of which is incorporated herein by way ofcross-reference.

The hybrid battery-supercapacitor allows the extended delivery of thecurrent demand during transmissions or other severe loads, without theterminal voltage dropping below an acceptable level.

The preferred embodiments provide a number of advantages, theseincluding:

Reduced voltage drop under load, giving extended run-time.

Reduced chance of battery damage from low voltage in Lithium-ionbatteries.

Reduced equivalent internal resistance compared with the battery alone.

Flexibility in design, as use can be made of smaller batteries thannormal, with higher internal resistance, at reduced cost.

Lithium ion batteries are widely used and, as stated above, are easilydamaged by high current pulses. These high current pulses cause largevoltage drops leading to premature shut down of the circuitry beingsupplied. These effects are both undesirable as they reduce battery lifeand battery run time. The preferred embodiments of the invention,however, use supercapacitors to reduce the effective resistive voltagedrop of the power supply combination and to reduce the capacitivevoltage drop. Accordingly, the run-time for portable battery powereddevices can be enhanced and premature shut down avoided.

By way of example, there is shown in FIG. 3 the discharge of a batterysupercapacitor combination. The battery was a Li Ion battery as used ona Nokia mobile telephone and which has an approximate internalresistance of 100 mΩ. The discharge was alternately “With” and “Without”a supercapacitor in parallel during a 1 A pulse discharge for 2 secondsduration, followed by 20 seconds off. The battery has been discharged toa state where it has little charge left, that is, when the potentialdifference is approximately 2.6 volts. The battery was then left tostand while the experiment was prepared and has recovered to asubstantially higher voltage. It is evident that the presence of thesupercapacitor in parallel with the battery provides a substantivedecrease in the resistive voltage drop.

FIG. 4 illustrates the characteristics of the voltage drops in greaterdetail.

The supercapacitor used to provide the results in FIGS. 3 and 4 had acapacitance of about 40 Farads and an ESR of about 5 mΩ.

The preferred embodiments of the invention are for use withbattery-powered devices that draw currents that vary greatly over time.For many devices, particularly mobile telephones, the variations occurover short time-scales during the normal operation of the telephone.

It will be appreciated that the losses in the power supply conductorsand the battery are proportional to the square of the current that flowsthrough these components. The losses therefore increase significantlyduring high-current pulses, even if these pulses are short in duration.However, the preferred embodiments, through the introduction of asupercapacitor, reduce these losses by reducing the effective resistanceof the power supply as seen by the load. That is, a supercapacitor, asused in the present embodiments, has properties of:

1. A low equivalent series resistance (ESR) relative to the internalresistance of the battery;

2. A high capacitance; and

3. The ability to carry a high current.

“Low ESR” means a value that is much lower than the internal resistanceof the battery. In one embodiment it has been found that benefit isderived where the ESR is half that of the internal resistance of thebattery. However, in more preferred embodiments, the ESR is about onequarter of the internal resistance of the battery preferably. In otherembodiments, the ESR is less than one tenth of the internal resistanceof the battery.

Capacitance is regarded as being “high” relative to the peak loadcurrents involved. There is no single value of capacitance that isconsidered “high”, but it would typically be a capacitance that issufficient to be able to supply the peak load current for up to severalseconds without becoming discharged. This is, however, also dependentupon the load characteristics. If the load will not ever demand such asupply of current then the supercapacitor need not be configured toprovide it.

A “high current” supercapacitor is regarded in this context as one thatis able to supply a load at least as great as that of the battery,usually many hundreds of milliamps (mA) to several amps or tens of amps,without sustaining any damage.

As referred to above, resistance losses increase with the square of thecurrent. Given this, a current with a given average value will generatehigher losses the greater the magnitude of variations in the current,because of the increased losses during current peaks. The inventionapplies this principle through the use of a supercapacitor that is ableto smooth the variations in a current to reduce the losses generated bythat current. That is, the internal resistance of a battery is thoughtto be a source of losses when current is drawn from the battery and thevariation in that current is reduced by the supercapacitor. The currentvariations are predominantly borne by the supercapacitor but, as it hasa much lower resistance, the losses generated are correspondinglysmaller. Stating this another way, the supercapacitor filters thecurrent waveform as seen by the battery in such a way that thesupercapacitor carries most of the rapid changes in load current. Duringoperation of the portable device, the battery will carry a current thathas a waveform with greatly reduced variations and a value that is muchcloser to the average load current than was the case without thesupercapacitor. Thus, the peak currents carried by the battery will bereduced significantly, reducing the losses in the power supply (theconductors and the supercapacitor) and protecting the battery from highcurrent pulses that are potentially harmful to it.

To optimise the benefit of the invention and the use of a supercapacitorto filter the current ripple, the preferred embodiments utilise lowresistance connections and conductors between the battery, thesuperconductor and the regulator circuitry from the portable device. Asa guide, the connection resistances should be in total a small fractionof the ESR of the supercapacitor. The conductors between thesupercapacitor and the load should have as low a resistance as caneconomically be achieved. As will be appreciated by the skilledaddressee, these parameters are varied to accommodate the inevitablecompromise between performance and cost.

When operating at low temperatures, such as −20° C., many types ofbattery, such as those using certain common Lithium-ion chemistry,cannot supply the current peaks required by their loads without theirvoltages dropping excessively. This causes the portable devices to turnoff before the batteries are actually depleted. In more extreme cases ithas been found that even fully charged batteries are prone to theselarge voltage drops. However, with use of the preferred embodiments ofthe invention, a power supply is provided which includes asupercapacitor that is connected in parallel with the battery. Thelow-pass filter effect of the supercapacitor—as described above—resultsin the battery being exposed to a reduced peak current. The battery thusprovides a current that is relatively constant and approximately equalto the average current drawn by the load, and the battery is able tocontinue to operate the portable device until it is either fullydepleted or unable to supply the lower, average current at the lowtemperature.

Many batteries contain electronic protection and control circuits thatcontrol the charging of the batteries, and/or protect the batteries fromhigh currents. While in some cases this circuitry is contained withinthe electronics of the load, in other cases it is contained within orattached to the housing of the battery. The protection and controlcircuits are commonly designed to disconnect that battery from the loador to limit the peak current drawn from the battery and/or to disconnectthe battery from the load if the battery's supply voltage drops below apredetermined value. Given this, some preferred embodiments of theinvention include a power supply having a battery of the type mentionedabove in parallel with a supercapacitor. This combination reduces therisk of the battery shutting down when unexpected large transientcurrents are drawn.

The filtering effect described above also allows an extension of therun-time of a device to be achieved. That is, the battery is able toreach a lower voltage than is otherwise possible before the system mustbe shut down.

In some embodiments the addition of a low-ESR supercapacitor in parallelwith the battery obviates the requirement for input-decouplingcapacitors. This, in turn, reduces costs for that part of the supply.

The low impedance of the supercapacitor also allows use of batterieswith higher impedance and greater capacity than normal. This increasesthe energy available to run the system, resulting again in increasedrun-times.

During operation of the power supply according to the preferredembodiments, the supercapacitor is effectively connected directly inparallel with the battery, as shown in FIG. 1. In some embodiments thereare one or more switches in the supply circuit to enable the electronicdevice to be switched ON and OFF. It will be appreciated that theseswitches preferably have a low ON-resistance relative to the ESR of thesupercapacitor. Preferably also, there is no switch between thesupercapacitor and the electronic device, as this will, in some cases,reduce the benefit obtained from the supercapacitor.

In other embodiments the power supply includes an additional circuit forcharging/discharging the supercapacitor gradually following theconnection of that supercapacitor to a battery that is providing adifferent voltage. That is, the circuit is to limit the charge/dischargecurrents that flow through the supercapacitor and the battery.

The conductors in which the greatest losses occur are those in which thehighest peak currents flow, all other things being equal. These are theconductors between the load and the supercapacitor. Therefore, to reducethese losses to a minimum, it is beneficial to place the supercapacitoras close as possible to the load. The conductors between the battery andthe supercapacitor carry a steadier current than the load current, andtherefore the losses in these conductors are reduced. For commonbattery-powered devices, peak load currents are usually high, at leastfor short periods. This is particularly true for pulsed load devicessuch as those utilising digital circuitry. The use of a suitablehigh-power supercapacitor in parallel with the battery, in accordancewith the invention, allows a reduction in the losses in the power systemand battery and helps to protect the battery from potentially harmfulcurrent pulses. This is achieved without requiring the use of expensiveelectronic circuitry and as the same time providing additional energystorage capacity for the device.

At low temperatures, a supercapacitor in accordance with the presentinvention also enables a portable electronic device to function normallywhen the battery would not be able to supply the peak current on itsown. That is, the use of the supercapacitor reduces the voltage dropthat is experienced at the supply terminals of the device and, hence,reduces the effect of a short transient peak load current from shuttingdown of the device.

A power supply according to the preferred embodiments also improves theaccuracy of detection of a low-battery condition, as the supercapacitorsmoothes the battery voltage. This helps avoid a premature shutdown, andextends the battery run-time.

In some embodiments of the invention, the supercapacitor is part of apower supply for a notebook computer that also supports the notebook'senergy requirements during a battery change without the need to shutdown or save data to disk. This functionality is more fully explored inthe co-pending PCT application filed with the Australian Patent Officeon 15 May, 2001 in the name of Energy Storage Systems Pty Ltd and whichis numbered PCT/AU/01/00554. The disclosure in that co-pendingapplication is incorporated herein by way of cross reference.

The power supply circuitry of the notebook computer was subject to someminor changes to the DC-DC converters to accommodate the supercapacitor.The result being an immediate increase in efficiency in the convertersof 5%, which translated to an increased run time of over 3 minutes percharge out of 83 minutes total run-time. The measurements were conductedon an Intel® Widbey platform using a Lithium ion battery with a 7.2 Ahcapacity in parallel with the supercapacitor. It will be appreciatedthat the Widbey platform operates on a supply voltage equal to twoLithium ion cells in series. This is generally lower than mostnotebooks, and provides cost savings in the simplifiedbattery-protection and balancing circuit. Costs are also reduced in theDC-DC converters, as a result of the low impedance of thesupercapacitor. That is, the need for the decoupling capacitors in theDC-DC converter is reduced if not eliminated. For example, some powerboards use as many as six decoupling capacitors.

Batteries designs have advanced mainly in the direction of increasingpower density to supply the demands of notebooks and other portabledevices. At face value this does not contribute to the availablerun-time for the device by the battery as there will be a compromise inthe stored energy for a given volume. However, due to the pulse natureof the usual loads being supplied by the battery, the effectiveness ofthat battery to contribute to the operation of the load is stronglydependent on its internal resistance. That is, the ability of thebattery to supply high power—even for short periods—is limited. This, intun, affects the efficiency and operation of the DC-DC converters in,say, a notebook PC. The protection circuits used in Lithium ion batterypacks further increase their effective internal resistance. Thepreferred embodiments of the invention, however, utilise a high-powersupercapacitor—that has very low ESR—in parallel with the battery. Thisprovides a hybrid supply that is able to make use of the combinedattributes of high energy density and low source impedance.

The design of a DC-DC converter, such as that used in a notebookcomputer, is influenced by the nature of the energy source and the load.The output load of the DC-DC converter is, in some cases, microprocessorcontrolled, with clock-gated technology to reduce average powerdissipation. Clock-gated architecture produces large transients at theoutput of the DC-DC converter and, consequently, produces large ripplecurrents in the power input rail of the converter. Although DC-DCconverters have local decoupling to filter out the transient pulses, thelimitations of conventional capacitors, cost and PCB real-estate,insufficient or improper local decoupling often allow most of thetransients to reach the battery and its protection circuits. As aresult, the battery-protection circuit prematurely shuts down thesystem, causing a loss in operational battery life.

With the use of the invention which, in this embodiment, includesplacing a low-impedance supercapacitor in parallel with the battery, thetransient is “filtered” prior to reaching the battery and its protectioncircuit. The voltage at the battery terminals and the protection circuitremains relatively constant, preventing the protection circuit fromgenerating a premature low-battery warning. This enables the powersupply to maximise the available capacity of the battery. For thisembodiment the overall improvement was found to be 5%, which results inan increased battery run-time of more than 3 minutes in an 83-minutenormal run-time. However, for another embodiment that utilised a largercapacity supercapacitor, the average increase was about 10% additionalrun-time.

As will be appreciated by the skilled addressee, from the teachingherein, that the actual improvement in the run-time provided by thesupercapacitor will be dependent upon a number of factors including thecharacteristics of the battery, the supercapacitor and the load.

The inclusion of the supercapacitor in parallel with the battery allowsfor modified charging algorithms, particularly for batteries of theLi-ion type. That is, the battery is able to be charged to full capacitymore quickly than could safely have been achieved in absence of thesupercapacitor.

The above tests were also conducted using the Intel® Whidbey platform.The platform operates on a supply voltage of two sets of four Lithiumion cells each, with the cells in each set in parallel. In othernotebook computers use is more typically made of three or four sets ofparallel pairs of Lithium ion cells connected in series. The inventionis suitable for use with both these battery configurations, as well asothers.

Typical notebook batteries have an internal resistance of over 100 mΩ,made up of:

1. The cells' internal resistance of about 50 mΩ for a single 1800 mAhcell, with typically three or more parallel pairs in series;

2. A 10 mΩ current-sense resistor; and

3. A 20 mΩ ON-resistance FET used as an output switch.

The internal resistance of a reduced-voltage battery, like that used inthe measurements referred to above, is about 63 mΩ. This is made up of aseries combination of two sets of three cells in parallel, plus thesense resistor and FET mentioned above. In use, the battery is comprisedof two parallel pairs in series which, together with the protectioncircuits, provide a total internal resistance of approximately 80 mΩ.

Connecting a supercapacitor—such as that manufactured by cap-XX Pty Ltdand designated as Mk 2 S/C—in parallel with the battery reduces thesource impedance still further. In this embodiment, the nominalresistance of the supercapacitor is less than 5 mΩ and, hence, theparallel combination of battery and supercapacitor is lower still. Sincethe supercapacitor's ESR is only about 6% of the battery's internalresistance, it is the supercapacitor that takes the brunt of all currentsurges. Consequently, whenever the load current increases suddenly, suchas during a CPU transient, the supercapacitor is able to provide most ofthe initial current surge. This smoothes the battery voltage and reducesbattery ripple current, resulting in increased accuracy of detection ofa low-battery condition.

The surge-current capability of the supercapacitor also reduces the I²Rlosses in all resistances between the supercapacitor itself and thebattery, including those in the battery, since the current peaks in thatpart of the circuit are reduced.

FIGS. 6 and 7 are comparative samples of the voltage and currentwaveforms in a power system of Intel® Whidbey Notebook Platformrespectively without and with a supercapacitor according to theinvention. For FIG. 6:

1. The top trace is the battery voltage.

2. The square wave is the load current, shown in 2 A/div.

3. The waveform superimposed on the square wave is the battery transientcurrent, shown in 500 mA/div; and

4. The bottom trace is a signal proportional to instantaneous powerdrawn from the battery, which is a product of battery voltage andcurrent. For FIG. 7:

1. The top trace is the battery voltage. Note that the inclusion of thesupercapacitor has eliminated the large ripple seen in FIG. 6, leavingonly a little high-frequency noise from the DC-DC converter;

2. The square wave is the load current, which is shown in 2 A/div;

3. The waveform superimposed on the square wave is the battery transientcurrent, and is shown in 500 mA/div. Note that the presence of thesupercapacitor has eliminated the major variations in battery currentseen in the corresponding trace in FIG. 6, leaving a nearly straightline;

4. The bottom trace is a signal proportional to the instantaneous powerdrawn from the battery and is a product of battery voltage and current.The supercapacitor has removed the large power variations visible inFIG. 6.

FIG. 8 is a graphical comparison of the instantaneous power drawn fromthe battery with and without a parallel supercapacitor The verticallines represent the range of instantaneous power drawn from the batteryand the horizontal marker on each represents the average power drawnduring the test.

The longest three vertical lines are the power drawn from the batteryalone in three separate tests. The power draw without a supercapacitorin parallel with the battery varied between 800 mW and 9500 mW. Theshortest three vertical lines are the range of power draw from thebattery itself when a supercapacitor was in parallel with it. Threedifferent supercapacitors were used, and the results were very similar,in spite of the range of ESR for the supercapacitors. This isattributable to the low ESR of all the supercapacitors, relative to theinternal resistance of the battery. From left to right, the supercapsidentified by the designations Mk2 S/C#1, Mk1 S/C#1 and Mk2 S/C#2 werecharacterised by approximate capacitances and ESRs of 40 Farads and 4mΩ, 50 Farads and 7.8 mΩ, and 50 Farads and 7.6 mΩ. Based upon theapproximate 80 mΩ internal resistance of the battery being used, thisresults in respective ratios of ESR to internal resistance of 5.0%, 9.8%and 9.5%.

In other embodiments use is made of higher-ESR supercapacitors due tolower cost. Notwithstanding, there is considerable gain to be had.

Supercapacitors for use in the preferred embodiments of the inventionare manufactured in accordance with the application. In some embodimentsthe supercapacitors are thin and light, with variable form-factors. Inother embodiments, however, the supercapacitors are contained within arigid housing. Single supercapacitor cells are rated for continuous useat 2.3 Volts, with a maximum of 2.5 Volts, although short transients athigher voltages are tolerable. For embodiments operating at highervoltages, the supercapacitor is made up of a series combination ofsupercapacitor cells.

The current rating of the supercapacitor is also determined by thenature of the application. While in some embodiments the charging,discharging or ripple currents are in the order of milliamps, in otherembodiments these currents are in the order of 20 Amps or more.

FIG. 9 is a table that provides two additional examples ofsupercapacitors that are applicable for use in a power supply accordingto the invention.

Previous investigations have shown that after a battery is discharged itwill eventually recover to be close to the initial voltage before thecurrent was drawn if the discharge is not too long or too deep. Thiseffect occurs due to concentration depletion of electroactive species atthe electrode surfaces within the battery during discharge. Once thedischarge ends then the molecules equilibrate to regenerate a uniformconcentration that is lower than the initial concentration due to theflow of electrons that occurred during the discharge. The discharge andthe equilibration are primarily diffusive and are therefore believedlikely to depend upon the square root of time.

Modelling battery behavior using Pspice enables some aspects of thisphenomenon to be explored. The present applicants commissioned such amodel to be investigated, and this was the subject of an unpublishedpaper by Dr J. G. Rathmell entitled “PSPICE MODELLING OFBATTERY/SUPERCAPACITOR DISCHARGE” dated 12 Jul. 1999. A copy of thispaper is incorporated as part of this specification and marked asAnnexure 1. The drawings referred to in Annexure 1 as “FIG. 1”, “FIG. 2”and so on are contained within this specification as part of the figuresand are labelled respectively as FIG. 16, FIG. 17 etcetera

This modelling has been applied by the inventors to develop thepreferred embodiments of the present invention. Particularly, themodelling was expanded upon and adapted to the case of a pulsed loadsuch as that used in a GSM type mobile telephone. In the battery model aRC circuit with a characteristic time constant and a look-up table areused to describe the effect. The modelling conditions involved the useof the AAA alkaline battery with the RMS rate loss model which has aninternal resistance of 0.6 ohm, a capacity of 1.2 Ah and a timeconstant, τ, of 10 seconds. Two values of IRATIO (I_(RMS)/I_(average))were used, a value of 1.02 to simulate a battery and supercapacitorcombination—as is achieved in practice—and 1.62 for the battery alonewith the average current being equal to 0.3 Amps based on a GSMwaveform.

FIG. 10 and FIG. 15 contains the results of the above modelling whichaccords with practical implementations of the preferred embodiments ofthe invention. That is, it is clearly demonstrated that the presence ofthe supercapacitor in parallel with the battery is beneficial because itreduces the depth of the discharge. Additionally, the effect of matchingthe discharge cycle to the battery recovery rate is shown. The useablecapacity is calculated from the time that it takes the discharge toreach down to 0.7 V and the total available time is obtained from therated capacity and the average current. In conclusion, while is betterto take a lot of “small bites” of energy rather than a few “big bites’of energy, there is still considerable benefit to be had from the use ofthe supercapacitor even if “big bites” are taken.

FIGS. 11 to 14 demonstrate the effect of on-time, expressed as afraction of the time constant, on the battery performance. Once againthe battery capacity is calculated from the rated capacity and theaverage current, the time constant of the battery is 10 seconds and theinternal resistance is 0.6 ohm. These graphs more clearly demonstratethe effect of minimizing the depth of discharge. It is also noticeablethat while the “supercapacitor advantage” is diminished under conditionswhere the “depletion” effect becomes apparent, there is stillconsiderable advantage to be gained.

Given the relationship between battery current, which is the subject ofthe investigation of the modelling referred to above, and the powerprovided by the battery, it becomes clear, from the teaching herein,that the power consumption characteristics shown in FIG. 8 are entirelyconsistent with the modelled current characteristics.

Although the invention has been described with reference to specificexamples, it will be appreciated by those skilled in the art that it maybe embodied in many other forms.

PSpice Modelling of Battery/supercapacitor Discharge Report ofInvestigation by Dr J G Rathmell 12, Jul. 1999 for cap-XX Pty Ltd

CONTENTS summary 3 introduction/scope 4 supercapacitor models 5 batterymodels 6 discharge simulation 8 discussion/further work 10 references 11FIG. 1 ac analysis 12 FIG. 2 transient analysis 13 FIG. 3 battery model14 FIG. 4 lost rate 15 FIG. 5 effect of RSER 16 FIG. 6 effect of CAP 17FIG. 7 10s simulation 18 FIG. 8 full discharge 19 Appendix 1 PSpice fileof FIG. 1 20 Appendix 2 PSpice file of FIG. 2 21 Appendix 3 PSpice fileof FIG. 5 22 Appendix 4 PSpice file of FIG. 6 23 Appendix 5 PSpice fileof FIG. 7 24 Appendix 6 PSpice file of FIG. 8 25 Appendix 7 modellibrary 26

Summary

A library of PSpice macromodels has been developed for supercapacitorsand batteries. Batteries covered are lead-acid, alkaline, Nicad, Nimhand Lithium-ion. These models have been modified to incorporate capacitylost under fast pulsing. Simulations have been done, demonstratingsupercapacitor impedance and phase, battery discharge and extension ofbattery life/capacity with supercapacitor.

Introduction/Scope

The scope of this report is the development of a library of PSpicebattery models and the investigation of PSpice simulation ofbattery/supercapacitor discharge under fast pulsing, in particular theextension of battery capacity by the use of a parallel supercapacitor.Battery models are for lead-acid, alkaline (N, AAA, AA, C, D & 9V),Nicad, Nimh and Lithium-ion. These models were largely gathered fromliterature [1-3], with modifications and corrections. Supercapacitormodels implemented are the RCCPE model provided by cap-XX [4]. Noverification of models with experiment was undertaken.

Supercapacitor Models

Supercapacitors are described in [4]. The model of supercapacitor, andparameters, used in simulation are as provided by cap-XX in [4] and incorrespondence. The model is a simple R, C plus constant phase term(RCCPE), describing frequency-dependent impedance; $\begin{matrix}{{Z(s)} = {R + \frac{1}{s\quad C} + \frac{1}{T\quad s^{P}}}} & (1)\end{matrix}$

where R is series equivalent resistance (SER), C capacitance, T amagnitude, P exponent and s=jω.

This model was implemented using the PSpice Laplace analog behaviouralmodelling form. Three forms of this model have been implemented; SUPER1directly specifying the equation SUPER2 incorporating a delay term andSUPER3 resolving the CPE term as separate real and imaginary terms (seeAppendix 7). These were for experimentation and are equivalent (exceptfor the delay). Also implemented is model RCTEST, a simple series RCcircuit for comparison with supercapacitor models.

Note that the CPE term is interpreted by PSpice as having a non-causalimpulse response, with a warning message given. A delay term (ε^(−so))is suggested by PSpice to resolve this. Such a delay alters simulationresults in ways that would require experimental verification. As thenon-causal impulse response is not a problem for the ac and transientanalyses done here, this warning is ignored. Ultimately, the RCCPE modelshould be altered to be applicable over the full frequency range thatPSpice considers, possibly by convolving the s-model with a suitablefilter function.

FIG. 1 shows impedance magnitude & phase as a function of frequency forthe three supercapacitor models and the RCTEST model. Models SUPER1 & 3are identical. These results compare with plots supplied by cap-XX. FIG.2 shows a transient analysis for the above model, with similar resultsas FIG. 1. PSpice source files used in these simulations are given inAppendices 1 & 2. Models are contained in Appendix 7.

Limitations of the models are that parameters are obtained from staticimpedance spectroscopy. A such, they do not incorporate non-linearitywith applied voltage nor rate-dependent anomalies. In particular, themodel has not been experimentally verified under the fast pulsing loadsdealt with here. Nonetheless, it is assumed that the models arereasonable.

Battery Models

Appendix 7 gives models for the batteries dealt with; lead-acid,alkaline (N, AAA, AA, C, D, & 9V), Nicad, Nimh and Lithium-ion. Thesemodels were obtained from [1-3]. Some debugging, correction modificationwas done. Six alkaline styles were done because of the slightlydifferent behaviours of these.

FIG. 3, from [1], shows the general form of these models. Models forNicad & Lithium-ion have additional terms for temperature. The Nicad &Nimh models also have correction terms for low-rate discharges.

All models consist of an output circuit (+OUTPUT, −OUTPUT) that involvesa battery voltage source and a series resistance. The V_Sense termsenses battery current for use in battery voltage correction. The restof a model is concerned with correction of the battery voltage withdischarge rate, temperature, age, etc. All use look-up tables to relatebattery voltage to these.

Of particular interest here is the E_Lost_Rate term which seeks to modelthe electrochemical reduction in avaliable battery capacity under heavydischarge. This is modelled as a non-linear function of the delayed (byRC delay) discharge rate using a look-up table. FIG. 4 shows the lostrate vs discharge rate for the batteries modelled.

In investigating the improvement of battery capacity with the use of asupercapacitor, it is principally lost rate that is involved. As FIG. 4shows, this reduction in battery capacity with discharge rate variesfrom 10%-80%, depending on battery type. Thus the effectiveness ofcoupling a supercapacitor with battery will be strongly dependent onbattery type and load. Note also that this lost capacity recovers intime if the load is removed, so we are primarily concerned here withcontinuous loads.

The delay and recovery time constants of the lost rate also variesconsiderably with battery type; from 3 s for Nicad, Nimh & Lithium-ion,10 s for alkaline to 60 s for lead-acid.

The battery models of Appendix 7 were designed to model discharge underrelatively constant loads (having variation times much greater than thelost rate time constants, i.e. frequencies much less than 1 Hz). Thiswork is concerned with pulsed current loads of frequency greater than100 Hz. With these, lost rate is a function of rms load current,although still with delayed onset [1]. At these frequencies,electrochemical recovery of lost capacity does not occur between pulses.

For relatively constant load current, average and rms are comparable,hence the extant models only relate lost rate to average current. Forthis work, these models have been modified to relate lost rate to therms load current, through modification of the delayed and averageddischarge rate used in lost capacity table look-up.

The circuit elements giving average lost rate are of the form:

E_Rate RATE 0 VALUE = { I(V_Sense) / CAPACITY } R_2 RATE 60 10 ; R2-C1-> 10 Second time constant C_1 60 0  1 * E_Lost_Rate 50 SOC TABLE {V(60) } = . . .

These have been modified as follows to give rms lost rate;

E_SQRate SQ_RATE 0 VALUE = { PWR ( I(V_Sense) / CAPACITY, 2 ) } R_SQSQ_RATE 60 10 ; R2-C1 -> 10 Second time constant C_SQ 60 0 1 * THIS NODEGIVES PROPER DISCHARGE RATE E_RATE RATE 0 VALUE = { SQRT( V(SQ_RATE) ) }R_RATE RATE 0 1G * E_Lost_Rate 50 SOC TABLE { SQRT( V(60) ) } = . . .

Appendix 7 contains two models for each battery type, MODEL_R andMODEL_A, using rms and average discharge rates respectively to calculatelost capacity. The _R models are used hereafter.

Temperature effects in the models already involve rms load current.

Discharge Simulation

The pulsed load used in this work is a pulsed current source, as mightbe expected to be drawn from a battery by a regulator or DC-DCconverter. The pulse timing was chosen to reflect what might be expectedof a GSM telephone handset; 0.577 ms timeslot for transmission in a4.615 ms frame [5], i.e. a short heavy discharge during transmissionfollowed by very light discharge. Load current amplitudes were chosen toillustrate the lost rate effects. These require experimentalverification.

The objective of this work is to demonstrate improvement in batterycapacity, with fast pulsing, by the use of a parallel supercapacitor.The battery effects of interest here are lost capacity, temperature andvoltage drop-out. Only lost capacity is investigated here, however,dealing with all three involves reducing battery pulse current amplitude(hence voltage drop) through the supercapacitor supplying the bulk ofthe pulse current and being recharged between pulses. Thus battery rmscurrent is reduced, reducing lost capacity and internal powerdissipation (temperature).

FIG. 5 shows an ALK_AA_R model with supercapacitor for a GSM loadperiod, for three different supercapacitor resistances R_(sup). Appendix3 shows the PSpice source file. The reduction of battery current pulseamplitude and of voltage drop is related to the relative size of R_(sup)compared to the battery resistance R_(bat). It is R_(bat)//R_(sup) thatdetermines the drop. Thus, for best results, R_(sup) is much less thanR_(bat).

FIG. 6 (and Appendix 4) shows the same simulation with three differentvalues of C_(sup). The supercapacitor time constant R_(sup)C_(sup)should be large enough to substantially maintain supercapacitordischarge for the duration of the pulse, and to spread the rechargingover the load period. Thus supercapacitor time constant should begreater than or equal to the load period.

FIG. 7 (and Appendix 5) shows pulsed discharge for the last cycle of a10 second simulation, for an ALK_AA_R battery model, with and withoutsupercapacitor. The supercapacitor used is the cap-XX E/Credit Card.

Of note here is the greater reduction in battery voltage and state ofcharge (capacity) for the case of no supercapacitor.

The ALK_AA_ battery model was used here as having a large loss rate withdischarge. The supercapacitor used was chosen as having an RC tocomplement this battery. The load current amplitudes were chosen (1A_(rms), 0.44 A_(average)) to give maximum lost rate of 60%.

From FIG. 7, the supercapacitor reduces the battery load to 0.45A_(rms).At this level, the lost rate is 36%. The limit of battery rms currentwould be, in this case, the load current average of 0.44 A. This wouldgive a lost rate of 35.4%.

Simulation time is a big issue here. The above 10 s simulation tookapproximately 1000 s on a Pentium 100 (HP Omni 800 ct). To simulate fullbattery discharge (several hours) would take over a week! The problem isthat simulation time is related to circuit node activity, as well ascircuit complexity. With fast pulsing, node status (voltage & current)is changing rapidly. The timestep of simulation must then be very small,relative to circuit time constants. Simulation takes approximately 0.5 sper load period and full discharge involves several million load pulses.

All is not lost. Of interest is the average current and the magnitude ofthe lost rates. The latter can be determined from FIG. 7. Battery modelshave been modified to incorporate a parameterIRATIO=I_(rms)/I_(average), with a default of 1. This is used to set thelost rate that would apply for a particular rms discharge rate, whensimulated under a constant load current I_(average). Under constantcurrent, simulation is very fast.

The previous circuit elements giving lost rate have been modified asfollows to give proper rms lost rate under constant current;

E_SQRate SQ_RATE 0 VALUE = { PWR( I(V_Sense) * IRATIO / CAPACITY, 2 ) }R_SQ SQ_RATE 60 10 ; R2-C1 -> 10 Second time constant C_SQ 60 0 1 * THISNODE GIVES PROPER DISCHARGE RATE E_RATE RATE 0 VALUE = { SQRT(V(SQ_RATE) ) } R_RATE RATE 0 1G * E_Lost_Rate 50 SOC TABLE { SQRT( V(60)) } = . . .

FIG. 8 (and Appendix 6) shows such a simulation, taking 4 seconds toexecute. Note that both cases (with & without supercapacitor) have thesame discharge rate, but the battery without the supercapacitor suffersfrom a greater lost rate. Hence its discharge life time is considerablyshorter (60% compared to 36%). This then demonstrates the increasedbattery life with supercapacitor.

Discussion/further Work

The battery models, with modifications for rms discharge lost rate,enable simulation of fast pulsed discharge, for both short and longdurations.

Limitations of this work are the lack of experimental verification ofboth battery and superconductor models under fast pulsing loads.

Further should involve;

verification of battery fast pulsing lost rate modelling,

improvement of battery models under fast pulsing, through measurementand model fitting,

extension of supercapacitor models for both non-linearity and ratedependencies, through measurement and model fitting, andaccuracy/granularity of the piece-wise linear table functionsrepresenting lost rate,

elaboration of supercapacitor design and application criteria for arange of batteries and loads (selection of supercapacitor R & C), and

measurement of real load currents.

References

1. “Simple PSpice models let you simulate common battery types”, S CHageman, EDN October 1993, pp117-132

2. “PSpice models nickel-metal-hydride cells”, S C Hageman, EDN Feb. 21995, p99

3. “A PSpice macromodel for lithium-ion batteries” S Gold, available athttp://www.polystar.com

4. “An introduction to cap-XX Pty Ltd and supercapacitors” cap-XX PtyLtd, January 1999

5. “General packet radio service in GSM” J Cai & D J Goodman, IEEECommunications Magazine, October 1997, pp122-131.

What is claimed is:
 1. An energy storage device for supplying a loadwith a pulsed load profile, the device including: a battery having apredetermined internal resistance R and two terminals for allowingelectrical connection to the battery; and a supercapacitor connected inparallel with the terminals and having a predetermined equivalent seriesresistance ESR, wherein ESR<0.25.R and a capacitance provided by thesupercapacitor is sufficient to limit the battery current to apredetermined maximum.
 2. A device according to claim 1 whereinESR<0.1.R.
 3. A device according to claim 1 wherein the supercapacitorprovides a substantially constant current as the energy storage devicedischarges.
 4. A device according to claim 1 including a housing forcontaining both the battery and the supercapacitor, the terminals beingaccessible from outside the housing for connecting to a load.
 5. A powersupply for a portable electronic device, the power supply including anenergy storage device according to claim
 1. 6. An energy storage devicefor supplying a load with a pulsed load profile, the device including: abattery for providing a battery current and having two terminals forelectrically connecting with a load; and a supercapacitor connected inparallel with the terminals and having a predetermined capacitance that,in use, independently limits the battery current to a predeterminedthreshold.
 7. A power supply including: a battery having two terminalsfor electrically connecting with a load that demands a pulsed current;and a supercapacitor connected in parallel with the terminals wherein acapacitance of the supercapacitor is sufficient to maintain the ratio ofthe range of instantaneous power provided by the battery and the averagevalue of the power provided by the battery at less than a predeterminedthreshold.
 8. A power supply according to claim 7 wherein thepredetermined threshold is one of the following: 1.5; 1; and 0.3.
 9. Anenergy storage device including: a battery having two terminals forelectrically connecting with a load that demands a pulsed current; and asupercapacitor connected in parallel with the terminals and having acapacitance sufficient to maintain the ratio of the range ofinstantaneous power provided by the battery and the average value of thepower provided by the battery at less than a predetermined threshold.10. An energy storage device according to claim 9 wherein thepredetermined threshold is one of 1.5; 1; and 0.3.
 11. An energy storagedevice for supplying a load with a pulsed load profile, the deviceincluding: a battery having a predetermined internal resistance R andtwo terminals for allowing electrical connection to the battery; and asupercapacitor connected in parallel with the terminals forindependently limiting the battery current to a predetermined maximum,the supercapacitor having a predetermined equivalent resistance ESR anda capacitance C, wherein ESR<0.5R and C is less than 1 Farad.
 12. Anenergy storage device for supplying a load with a pulsed load profile,the device including: a battery having a predetermined internalresistance R and two terminals for allowing electrical connection to thebattery; and a supercapacitor connected in parallel with the terminalsfor independently limiting the battery current to a predeterminedmaximum, the supercapacitor having a predetermined equivalent seriesresistance ESR, wherein ESR<110 mOhms<R.
 13. A device according to claim12 wherein the ESR is less than about 50 mOhms.
 14. A device accordingto claim 12 wherein the ESR is less than about 30 mOhms.
 15. An energystorage device for supplying a load with a pulsed load profile, thedevice including: a battery having a predetermined internal resistance Rand two terminals for allowing electrical connection to the battery; anda supercapacitor connected in parallel with the terminals forindependently limiting the battery current to a predetermined maximum,the supercapacitor having a predetermined equivalent series resistanceESR, a predetermined volume V and a predetermined capacitance C, whereESR<0.5.R, V<13 cm³ and C>1 Farad.
 16. An energy storage device forsupplying a load with a pulsed load profile, the device including: abattery having two terminals for allowing electrical connection to thebattery; and a supercapacitor for independently limiting the batterycurrent to a predetermined maximum, the supercapacitor having aplurality of serial connected supercapacitor cells for connecting inparallel with the terminals, wherein the supercapacitor cells have anoperating voltage of at least 2.3 Volts and the supercapacitor has apredetermined equivalent series resistance ESR of less than about 20mOhms.
 17. A device according to claim 16 wherein ESR is less than about15 mOhms.
 18. An energy storage device for supplying a load with apulsed load profile, the device including: a battery having twoterminals for allowing electrical connection to the battery; and asupercapacitor for independently limiting the battery current to apredetermined maximum, the supercapacitor having a plurality of serialconnected supercapacitor cells for connecting in parallel with theterminals, wherein the supercapacitor cells have an operating voltage ofat least 2.3 Volts and the supercapacitor has a predeterminedcapacitance of greater than about 1.9 Farads.